调频输入正弦锁相环路的定性分析

<正> §1.引言正如文献1]中指出:锁相技术作为一门新技术,近几年来在无线电通讯、雷达、空间技术等各方面都已得到广泛地应用,很多实际和理论工作者都是从事于二阶锁相环路的设计和理论分析。文献2]对具有正切鉴相特性和调频输入锁相环路方程及其推广的Lienard方程作了系统的研究,本文利用类似于文献2]3]所采用的传统的定性方法考虑了实践

QUALITATIVE ANALYSIS OF A P-L-L WITH SINE DISCRIMINATOR AND FREQUENCY MODULATION INPUT

By using the traditional qualitative method, in this paper, the anthor considers two phase locked loop equations as follows: (d~2φ)/(dt~2)+α(dφ)/(dt)+γsinφ=β_1+β_2(αsinΩ_Mt+Ω_McosΩ_Mt) (Ⅰ) and (d~2φ)/(dt~2)+(α+ηcosφ)(dφ)/(dt)+γsinφ=β_1+β_2(αsinΩ_Mt+Ω_McosΩ_Mt) (Ⅱ) where α>o, η≥o, γ>o, β_1>o, β_2>o, Ω_Mo, and the function α+ηcoscφ might change its sign. As to Eqs. (Ⅰ) and(Ⅱ), the anthor provides sufficient conditions for the existence of a periodic solution with period(2π)/Ω, and proves that this periodic soIution tends to the origin as β_1→o, β_2→o, and also the local uniqueness and asymptotic stability of this periodic soluion for β_1, and β_2 small enough.